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### Finding the Period of a Squared Trig Function

```Date: 08/28/2006 at 22:54:11
From: robyn
Subject: Determining the period of trigonometric equations

How do you find the period of a cosine equation when the cosine is
squared?  For example, 3 - 2cos^2(pi(x)/3).

Every attempt I've made has given me a period of 2pi, and I know it is
supposed to be 3.  I tried breaking it into cos(x) * cos(pi/3), but
that is not correct.  I cannot figure out how the squared affects the
graph.

```

```
Date: 08/29/2006 at 10:13:33
From: Doctor Fenton
Subject: Re: Determining the period of trigonometric equations

Hi Robyn,

Thanks for writing to Dr. Math.  You need to use one of the Double
Angle identities (or a Half Angle identity, depending upon your point
of view) to rewrite cos^2(t) as a trigonometric function to the first
power, instead of being squared.  Then you should be able to determine
the period.

If you are not familiar with the identities, they are listed on

Trig Identities
http://mathforum.org/dr.math/faq/formulas/faq.trig.html#identities

If you have any questions or need more help, please write back and
show me what you have done, and I will try to offer further
suggestions.

- Doctor Fenton, The Math Forum
http://mathforum.org/dr.math/

```

```
Date: 08/29/2006 at 18:20:56
From: robyn
Subject: Thank you (Determining the period of trignomonic equations)

THANK YOU SOOO MUCH!  I have been working on an AP Calc packet for
days and could not figure out that problem.  Thanks a million times!
```
Associated Topics:
High School Trigonometry

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